Method of adjusting projection optical apparatus

ABSTRACT

This invention relates to an adjusting method for correcting the random component of distortion of a projection optical apparatus without performing complicated assembly and adjustment. This adjusting method has the first step of measuring the residual distortion component of a projection optical system having a predetermined target member in its optical path, the second step of calculating, based on the measurement result of the first step, the surface shape of the target member to cancel the residual distortion component, the third step of removing the target member from the projection optical system and machining the target member so as to have the surface shape calculated in the second step, and the fourth step of inserting the target member machined in the third step into the optical path of the projection optical system.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a projection optical apparatusfor projecting and exposing the pattern of a first object on a secondobject and, more particularly, to a method of adjusting the projectionoptical apparatus.

[0003] 2. Related Background Art

[0004] A projection optical system used in an exposure apparatus thatprints a precision circuit pattern on a substrate (wafer, plate, or thelike) coated with a photosensitive material requires very high opticalperformance. For this purpose, optical members used in the projectionoptical system are manufactured with an ultimately high manufacturingprecision.

[0005] When manufactured optical members are combined to assemble aprojection optical system, very fine adjustment is performed such asadjusting the distances between the respective optical members bychanging the thicknesses of washers between lens barrels holding therespective optical members, tilting the optical members (rotating theoptical members about, as an axis, a direction perpendicular to theoptical axis), or shifting the optical members (moving the opticalmembers in a direction perpendicular to the optical axis), whileactually measuring the aberration of the projection optical system. Thisadjustment minimizes degradation in optical performance which is causedby the manufacturing error of the optical members or which occurs duringassembly of the optical members.

SUMMARY OF THE INVENTION

[0006] According to the present invention, there is provided anadjusting method having the first step of measuring the residualdistortion component of a projection optical system having apredetermined target member in its optical path, the second step ofcalculating, based on the measurement result of the first step, thesurface shape of the target member which cancels the residual distortioncomponent, the third step of removing the target member from theprojection optical system and machining the target member so as to havethe surface shape calculated in the second step, and the fourth step ofinserting the target member machined in the third step into the opticalpath of the projection optical system.

[0007] The present invention will be more fully understood from thedetailed description given hereinbelow and the accompanying drawings,which are given by way of illustration only and are not to be consideredas limiting the present invention.

[0008] Further scope of applicability of the present invention willbecome apparent from the detailed description given hereinafter.However, it should be understood that the detailed description andspecific examples, while indicating preferred embodiments of theinvention, are given by way of illustration only, since various changesand modifications within the spirit and scope of the invention will beapparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009]FIGS. 1 and 2 are views for explaining the principle of anadjusting method according to the present invention, in which FIG. 1shows the state of a beam before adjustment, and FIG. 2 shows the stateof a beam after adjustment;

[0010]FIG. 3 shows the schematic arrangement of an exposure apparatus towhich the adjusting method of the present invention is applied;

[0011]FIG. 4 shows the arrangement of a holding member that holds adistortion correction plate;

[0012]FIG. 5 is a plan view showing the arrangement of a test reticleused for measuring various aberrations other than distortion;

[0013]FIG. 6 is a plan view showing the arrangement of a test reticleused for measuring distortion;

[0014]FIG. 7 shows the state of a pattern on a wafer which is formed byusing the test reticle shown in FIG. 6;

[0015]FIGS. 8 and 9 are graphs for explaining a curved surfaceinterpolation equation of this embodiment, in which FIG. 8 shows a casewherein a conventional curved surface interpolation equation is used,and FIG. 9 shows a case wherein a curved surface interpolation equationof this embodiment is used;

[0016] FIGS. 10 to 14 show a curved surface interpolation method of thisembodiment;

[0017]FIG. 15 shows the arrangement of an apparatus that machines thedistortion correction plate;

[0018]FIG. 16 briefly shows the adjusting method according to thepresent invention; and

[0019]FIG. 17 briefly shows a method of calculating the shape of thedistortion correction plate from distortion data.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0020] In the conventional projection optical system, distortioncomponents are present that cannot be corrected even by assemblyadjustment as described above. Of all the distortion components,regarding in particular a random component (asymmetric distortion) nothaving a directionality with respect to an optical axis serving as thereference, no effective correcting method is conventionally availablefor such a random component, and this random component interferes withan improvement in total overlay of a precision printing exposureapparatus.

[0021] On the other hand, in the present invention having the abovearrangement, as the surface of a target member serving as an opticalmember partly constituting the projection optical system is machined, abeam that passes through this target member can be deflected byrefraction. Thus, an imaging position at a predetermined point on thesurface of an object is deflected on an image surface in a directionperpendicular to the optical axis, so that a residual magnificationcomponent and a residual distortion component in the projection opticalsystem can be corrected.

[0022] Assuming an ideal imaging position of a projection optical systemwhich is an ideal optical system having no aberration, a residualdistortion component is a shift amount between the actual imagingposition of a beam formed through a target member and a projectionoptical system, and an ideal imaging position.

[0023] The principle of the present invention will be described withreference to the accompanying drawings. FIG. 1 is a view showing atarget member 10 before machining arranged between a reticle R and awafer W. In FIG. 1, the projection optical system is omitted. Referringto FIG. 1, a beam emerging from a point O on the reticle R forms animage on the wafer W through the target member 10 and the projectionoptical system (not shown). When the projection optical system (notshown) has distortion, the beam emerging from the point O on the reticleR is focused on a point P₁ to form the image of the point O at the pointP₁. When the projection optical system (not shown) is an ideal imagingoptical system, a beam emerging from the point O on the reticle R isfocused on a point P₀ to form the image of the point O at the point P₀.At this time, the shift between the points P₀ and P₁ within the surfaceof the wafer W corresponds to the distortion of the projection opticalsystem.

[0024] In the present invention, as shown in FIG. 2, the surface of thetarget member 10 present in the optical path of the projection opticalsystem is machined so that it is changed from a surface 10 a beforemachining to a surface 10 b. Then, the beam emerging from the point O onthe reticle R is refracted by the surface 10 b of the target member 10,and is thus focused on the point P₀ on the wafer W. Hence, thedistortion of the projection optical system is corrected.

[0025] In the present invention, it is desirable that the variousaberrations that occur symmetrically with respect to the optical axisare corrected before correction by means of the target member isperformed. Then, the machining amount of the target member can bedecreased, so that machining becomes easy, and the influence ofmachining on other aberrations can be prevented.

[0026] In the present invention, it is preferable that the projectionoptical system is constituted to sequentially have a front group, anaperture stop, and a rear group in this order from the object side. Atthis time, it is preferable that the target member be arranged in one ofthe front and rear groups, through which a beam having a smallernumerical aperture passes. With this arrangement, the target member isarranged at a position where the beam has a small spot size for thepurpose of imaging. Therefore, the control precision of the residualmagnification component and the residual distortion component can befurther improved. Furthermore, with this arrangement, the influence ofthe adjusting method of the present invention on other aberrationcomponents can be decreased.

[0027] The present invention is preferably arranged such that the targetmember is located in the front or rear group and farthest from theaperture stop. With this arrangement, the target member is provided at aposition where the beam has a small spot size for the purpose ofimaging. Therefore, the control precision of the residual magnificationcomponent and the residual distortion component can be further improved.Furthermore, in this arrangement, since the target member is located atthe outermost position (closest to the object or the image) of theprojection optical system, the arrangement of the lens barrels of theprojection optical system can be simplified, thereby facilitatingremoved and insertion of the target member in the third and fourthsteps.

[0028] The present invention preferably satisfies an inequality:

d/f<0.07  (1)

[0029] where d is the distance between an optical member adjacent to atarget member and this target member, and f is the focal length of thegroup in which the target member is located.

[0030] This conditional inequality (1) defines the appropriatearrangement of the target member. When this conditional inequality (1)is not satisfied, the operational distance of the projection opticalsystem cannot be sufficiently maintained, which is not preferable. Inthe conditional inequality (1), it is preferable that the lower limit ofd/f be set to 0.001 to satisfy 0.001<d/f. If d/f exceeds this lowerlimit, it may cause interference between a holding member that holds thetarget member and a holding member that holds an optical member adjacentto the target member. Then, the degree of freedom in design of theholding members is decreased, which is not preferable.

[0031] The present invention preferably satisfies an inequality:

−0.005<Φ<0.005  (2)

[0032] where Φ is the refracting power of the target member. Therefracting power Φ of the target member is expressed by Φ=1/fa where fais the focal length of the target member.

[0033] This conditional inequality (2) defines the range of appropriaterefracting powers Φ of the target member so that the target member canbe easily mounted. If the target member has a refracting power exceedingthe range of the conditional inequality (2), the decentering allowed forthe target member becomes strict. Then, the target member must bepositioned (the optical axis of the target member must be adjusted) athigh precision, which is not preferable. If the refracting power Φ ofthe target member falls within the range of the conditional inequality(2), the influence of aberrations caused by the mounting error of thetarget member can be decreased, and the positioning precision of thetarget member can be set to almost equal to the machining precision ofthe holding member of the target member. When these points and easymachinability are considered, the target member is preferablyconstituted by a plane-parallel plate having no refracting power.

[0034] The preferred embodiment of the present invention will bedescribed in detail with reference to the accompanying drawings. FIG. 3is a diagram schematically showing an arrangement of an exposureapparatus suitably applied to a projection optical apparatus of thepresent invention. The coordinate system is set as shown in FIG. 3.

[0035] Referring to FIG. 3, an illumination optical unit IS uniformlyilluminates a reticle R placed on a reticle stage RS with exposurelight, e.g., a 365-nm i line, a 248-nm KrF excimer laser, and a 193-nmArF excimer laser. A distortion correction plate 10 serving as thetarget member, a holding member 11 for placing the distortion correctionplate 10 thereon, and a projection objective lens (projection opticalsystem) PL having a predetermined reduction magnification andsubstantially telecentric on its two sides are provided below thereticle R. The projection objective lens PL sequentially has a frontgroup G_(F) of positive refracting power, an aperture stop AS, and arear group G_(R) of positive refracting power in this order from thereticle R side, and the ratio in refracting power of the front groupG_(F) to the rear group G_(R) corresponds to the reduction magnificationof the projection objective lens PL. In this embodiment, the projectionobjective lens PL is optically designed such that its aberration iscorrected including that of the distortion correction plate 10.Accordingly, light from the reticle R illuminated by the illuminationoptical unit IS reaches a wafer W placed on a wafer stage WS through thedistortion correction plate 10 and projection objective lens PL, andforms a reduced image of the reticle R on the wafer W. This wafer stageWS is movable in the X, Y, and Z directions. In this embodiment, thedistortion correction plate 10 is constituted by a plane-parallel platemade of a material, e.g., silica glass, that transmits exposure lighttherethrough.

[0036] As shown in, e.g., FIG. 4, the holding member 11 on which thedistortion correction plate 10 is placed has an opening for passingexposure light therethrough, and pins 11 a to 11 c for regulating thedistortion correction plate 10 are provided on part of the holdingmember 11. Accordingly, when the distortion correction plate 10 isabutted against the pins 11 a to 11 c, the distortion correction plate10 is positioned.

[0037] In this embodiment, of the various aberrations of the projectionobjective lens PL, symmetrical components are corrected prior to therandom component of the distortion. First, a test reticle TR₁ formedwith a predetermined pattern is placed on the reticle stage RS. As shownin, e.g., FIG. 5, the test reticle TR₁ has a pattern area PA₁ providedwith a plurality of marks and a light-shielding band LST surrounding thepattern area PA₁. The test reticle TR₁ is subjected to Koehlerillumination with the exposure light emerging from the illuminationoptical unit IS. Light emerging from the illuminated test reticle TR₁reaches the wafer W coated with a photosensitive material, e.g., aresist, through the distortion correction plate 10 and projectionobjective lens PL, and forms the pattern image of the test reticle TR₁on the wafer W. Thereafter, the wafer W is developed, and the resistpattern image obtained by this development is measured by a coordinatemeasuring machine. The distances between the optical members and thetilt shift of the optical members are adjusted based on the informationon the measured resist pattern image, thereby correcting the variousaberrations other than the random component of the distortion.

[0038] After the various aberrations other than the random component ofthe distortion are corrected, the random component of the distortion iscorrected.

[0039] A test reticle TR₂ as shown in FIG. 6 is placed on the reticlestage RS in place of the test reticle TR₁ used for above correction. Thetest reticle TR₂ has a plurality of cross marks M_(0,0) to M_(8,8)arranged in a matrix form, i.e., arranged on the lattice points ofsquare lattices, within a pattern area PA₂ surrounded by alight-shielding band LST that shields exposure light. The cross marksM_(0,0) to M_(8,8) of the test reticle TR₂ may be formed on the patternarea PA₁ of the test reticle TR₁. In other words, both the test reticlesTR₁ and TR₂ may be employed simultaneously.

[0040] As shown in FIG. 3, the test reticle TR₂ on the reticle stage RSis illuminated with the exposure light of the illumination optical unitIS. Light from the test reticle TR₂ reaches the exposure area on thewafer W whose surface is coated with the photosensitive material, e.g.,the resist, through the distortion correction plate 10 and projectionobjective lens PL, and forms the latent images of the plurality of crossmarks M_(0,0) to M_(8,8) of the test reticle TR₂ on the wafer W. Theexposed wafer W is developed, and the plurality of exposed cross marksM_(0,0) to M_(8,8) are patterned.

[0041]FIG. 7 shows the plurality of patterned cross marks in an exposurearea EA on the wafer W. In FIG. 7, ideal imaging positions where imagesare formed when the projection optical system is an ideal optical system(an optical system having no aberrations) are expressed by intersectionpoints of broken lines. In FIG. 7, a cross mark P_(0,0) corresponds tothe image of the cross mark M_(0,0) on the reticle R, a cross markP_(1,0) corresponds to the image of the cross mark M_(1,0) on thereticle R, and a cross mark P_(0,1) corresponds to the image of thecross mark M_(0,1) on the reticle R. Any other cross mark M_(i,j) andcross mark P_(i,j) correspond to each other in the same manner.

[0042] The X- and Y-coordinates of each of the plurality of cross marksP_(0,0) to P_(8,8) formed on the wafer W are measured by the coordinatemeasuring machine.

[0043] In this embodiment, beams emerging from the plurality of crossmarks M_(0,0) to M_(8,8) and focused on the plurality of cross marksP_(0,0) to P_(8,8) are shifted to ideal imaging positions by machiningthe surface of the distortion correction plate 10. The calculation ofthe surface shape of the practical distortion correction plate 10 willbe described.

[0044] As shown in FIG. 3, the distortion correction plate 10 of thisembodiment is arranged in the optical path between the projectionobjective lens PL and the reticle R. This position is a position where abeam having a comparatively smaller numerical aperture (N.A.) passes.Thus, in shifting the imaging positions by the distortion correctionplate 10, only shifting of the principal ray of the beam shifted bychanging the surface shape of the distortion correction plate 10 need berepresentatively considered.

[0045] A relationship expressed by an equation:

w=β·L _(R)·(n−1)·θ  (3)

[0046] is established where w is a distortion amount which is a shiftamount between the ideal imaging positions and the plurality of crossmarks P_(0,0) to P_(8,8) shown in FIG. 7, and θ is the change amount ofangle of the normal to the surface of the distortion correction plate 10at a principal ray passing point where each of the principal rays fromthe plurality of cross marks M_(0,0) to M_(8,8) passes through thedistortion correction plate 10. The angle change amount θ concerns thenormal to the surface of the distortion correction plate 10 in areference state before machining, β is the lateral magnification of theprojection optical system, L_(R) is a distance between the reticle R andthe machining target surface of the distortion correction plate 10 alongthe optical axis, and n is the refractive index of the distortioncorrection plate 10. In equation (3), the machining target surface ofthe distortion correction plate 10 is on the wafer W side.

[0047] When the distortion correction plate 10 is located in the opticalpath between the projection objective lens PL and wafer W, arelationship satisfying an equation:

w=L _(w)·(n−1)·θ  (4)

[0048] is established where L_(w) is a distance between the wafer W andthe machining target surface of the distortion correction plate 10 alongthe optical axis.

[0049] Therefore, the plane normals at principal ray passing points onthe surface of the distortion correction plate 10 can be obtained fromthe distortion amount as a shift amount between the coordinates of theplurality of cross marks P_(0,0) to P_(8,8) measured by the coordinatemeasuring machine described above and the ideal imaging positions.

[0050] Although the plane normals at the respective principal raypassing points of the distortion correction plate 10 are determined bythe above procedure, the surface of the distortion correction plate 10cannot be obtained as a continuous surface. Therefore, in thisembodiment, a continuous surface shape is obtained from the planenormals at the principal ray passing points of the distortion correctionplate 10 that are obtained by the equation (3) or (4), by using a curvedsurface interpolation equation.

[0051] Various types of curved surface interpolation equations areavailable. In this embodiment, since plane normals are known and thetangential vectors of the surface at the principal ray passing pointscan be calculated from the plane normals, as the curved surfaceinterpolation equation used in this embodiment, the Coons' equation issuitable which extrapolates a curved surface with the coordinate pointsand tangential vectors of these coordinate points. For example, however,if the tangential vectors θ₀ and θ₁ of adjacent coordinate points Q₀ andQ₁ are equal, as shown in FIG. 8, the extrapolated curved line (curvedsurface) may wave.

[0052] In this embodiment, when the distortion amounts caused by theprincipal rays that pass through adjacent principal ray passing pointsare equal, it is effective to equalize the distortion amounts of theseadjacent principal ray passing points. If the extrapolated curved line(curved surface) waves, as shown in FIG. 8, the amounts and directionsof distortion at adjacent principal ray passing points change over time.Then, not only the random component of the distortion cannot becorrected, but also a random component of this type might be furthergenerated undesirably.

[0053] Hence, in this embodiment, in order to equalize the distortionamounts of adjacent principal ray passing points as well, as shown inFIG. 9, the vector component in the Z direction of a tangential vectorθ₀ at the coordinate point Q₀ is added, as a height Z₁ in the Zdirection, to the coordinate point Q₁ adjacent to the coordinate pointQ₀. Then, even if the tangential vectors of the adjacent coordinatepoints Q₀ and Q₁ are equal, the extrapolated curved line becomes almostlinear between these coordinate points Q₀ and Q₁, and the principal rayspassing between these coordinate points Q₀ and Q₁ are refracted atalmost the same angles. Accordingly, when the distortion amounts of theadjacent principal ray passing points are equal, the distortion amountscan be equalized between these points as well.

[0054] The procedure of curved surface complement of this embodimentwill be described in detail with reference to FIGS. 10 to 14. An X-Y-Zcoordinate system is set as shown in FIGS. 10 to 14.

[0055] [Step 1]

[0056] As shown in FIG. 10, an X-Y-Z coordinate system is defined on atarget surface 10 a of the distortion correction plate 10. In FIG. 10,principal ray passing points Q_(0,0) to Q_(8,8), through which theprincipal rays of the beams propagating from the plurality of crossmarks M_(0,0) to M_(8,8) shown in FIG. 6 toward the plurality of crossmarks P_(0,0) to P_(8,8) shown in FIG. 7 pass, are expressed byintersection points of broken lines. The normal vectors at therespective principal ray passing points Q_(0,0) to Q_(8,8) obtained bythe above equation (3) are expressed as θ_(i,j) (note that in thisembodiment i=0 to 8 and j=0 to 8, that is, θ_(0,0) to θ_(8,8), and thatthe X-and Y-components of vector θ_(i,j) are defined as zero when thedirection of the normal vector θ_(i,j) is equal to the direction of theoptical axis), and the heights of the normal vectors in the Z directionat the respective principal ray passing points Q_(0,0) to Q_(8,8) areexpressed as Z_(i,j) (note that in this embodiment i=0 to 8 and j=0 to8, that is, Z_(0,0) to Z_(8,8)).

[0057] [Step 2]

[0058] As shown in FIG. 11, of the principal ray passing points, theprincipal ray passing point Q_(0,0) at the end point of the Y-axis isdefined as the reference in the Z-axis direction, and is set asZ_(0,0)=0.

[0059] [Step 3]

[0060] The height Z_(0,1) in the Z direction of the tangential vector atthe principal ray passing coordinate point Q_(0,1) adjacent to theprincipal ray passing point Q_(0,0) on the Y-axis is calculated, basedon the normal vector θ_(0,0) of the principal ray passing point Q_(0,0),by the following equation (5):

Z _(0,j) =Z _(0,j−1) +θy _(0,j−1)·(y _(0,j) −y _(0,j−1))  (5)

[0061] where θy_(0,j): the vector component in the Y-axis direction ofthe normal vector θ_(0,j) at the principal ray passing point Q_(0,j)

[0062] y_(0,j): the component in the Y-axis direction of the coordinatesof the principal ray passing point Q_(0,j) obtained when the principalray passing point Q_(0,0) is set as the origin

[0063] In step 3, the height Z_(0,1) in the Z direction of thetangential vector at the principal ray passing point Q_(0,1) iscalculated based on the above equation (5) as follows

Z _(0,1) =Z _(0,0) +θy _(0,0)·(y _(0,1) −y _(0,0))

[0064] [Step 4]

[0065] The heights Z_(0,2) to Z_(0,8) in the Z direction of thetangential vectors at the principal ray passing points Q_(0,2) toQ_(0,8) on the Y-axis are calculated based on the above equation (5) inthe same manner as in step 3.

[0066] [Step 5]

[0067] The height Z_(1,0) in the Z direction of the tangential vector atthe principal ray passing coordinate point Q_(1,0) adjacent to theprincipal ray passing point Q_(0,0) on the X-axis is calculated, basedon the normal vector θ_(0,0) of the principal ray passing point Q_(0,0),by the following equation (6):

Z _(i,0) =Z _(i−1,0) +θx _(i−1,0)·(x _(i,0) −x _(i−1,0))  (6)

[0068] where θx_(i,0): the vector component in the X-axis direction ofthe normal vector θ_(i,0) at the principal ray passing point Q_(i,0)

[0069] x_(1,0): the component in the X-axis direction of the coordinatesof the principal ray passing point Q_(i,0) obtained when the principalray passing point Q_(0,0) is set as the origin

[0070] In step 5, the height Z_(1,0) in the Z direction of thetangential vector at the principal ray passing point Q_(1,0) iscalculated based on the above equation (6) as follows

Z _(1,0) =Z _(0,0) +θx _(0,0)·(x _(1,0) −x _(0,0))

[0071] [Step 6]

[0072] The heights Z_(2,0) to Z_(8,0) in the Z direction of thetangential vectors at the principal ray passing points Q_(2,0) toQ_(8,0) on the X-axis are calculated based on the above equation (6) inthe same manner as in step 5.

[0073] [Step 7]

[0074] As shown in FIG. 12, the heights Z_(i,j) in the Z direction ofthe tangential vectors at the principal ray passing points Q_(1,1) toQ_(8,8) located between the X- and Y-axes are sequentially calculatedstarting with the one closer to the origin Q_(0,0) based on thefollowing equation (7):

Z _(i,j) ={[Z _(i−1,j) +θx _(i−1,j)·(x _(i,j) −x _(i−1,j)]) +[Z _(i,j−1)+θy _(i,j−1)·(y _(i,j) −y _(i,j−1))]}/2  (7)

[0075] In step 7, first, the height Z_(1,j) in the Z direction of thetangential vector at the principal ray passing point Q_(1,1) closest tothe origin Q_(0,0) is calculated. Z_(1,1) is calculated based on theequation (7) as follows

Z _(1,1) ={[Z _(0,1) +θx _(0,1)·(x _(1,1) −x _(0,1))]+[Z _(1,0) +θy_(1,0)·(y _(1,1) −y _(1,0) )]}/2

[0076] In step 7, as shown in FIG. 13, after the height Z,_(1,1) in theZ direction of the tangential vector at the principal ray passing pointQ_(1,1) is calculated, the heights Z_(1,2), Z_(2,1), Z_(2,2), . . . ,Z_(i,j), . . . , and Z_(8,8) in the Z direction of the tangentialvectors at the principal ray passing points Q_(1,2), Q_(2,1), Q_(2,2), .. . , Q_(i,j), . . . , and Q_(8,8) are sequentially calculated startingwith the one closer to the origin Q_(0,0) based on the above equation(7).

[0077] [Step 8]

[0078] Based on the heights Z_(0,0) to Z_(8,8) at the principal raypassing points Q_(0,0) to Q_(8,8) obtained through steps 1 to 7, the X-and Y-coordinates of the principal ray passing points Q_(0,0) toQ_(8,8), and the tangential vectors at the principal ray passing pointsQ_(0,0) to Q_(8,8) obtained from the plane normal vectors θ_(0,0) toθ_(8,8) at the principal ray passing points Q_(0,0) to Q_(8,8), a curvedsurface is formed in accordance with the Coons' patching method. Morespecifically, the control points of the Coons' patching method aredetermined as the X-, Y-, and Z-coordinates of the principal ray passingpoints Q_(0,0) to Q_(8,8), and the tangential vectors of the controlpoints are determined as the tangential vectors calculated from theplane normal vectors θ_(0,0) to θ_(8,8) at the principal ray passingpoints Q_(0,0) to Q_(8,8).

[0079] A curved surface as shown in, e.g., FIG. 14, can be obtained bycurved surface interpolation in accordance with the Coons' patchingmethod of step 8.

[0080] In above steps 1 to 8, the height Z_(0,0) in the Z direction ofthe tangential vector at the point Q_(0,0) located at the edge of thetarget surface 10 a is set as 0 (step 2), the heights Z_(0,1) to Z_(0,8)and Z_(1,0 l to Z) _(8,0) in the Z direction of the tangential vectorsat the points Q_(0,1) to Q_(0,8) and the points Q_(1,0) to Q_(8,0) onthe Y- and X-axes, respectively, present at the edges of the targetsurface 10 a are calculated (steps 3 to 6), and thereafter the heightsZ_(i,j) (i≠0, j≠0) in the Z direction of the tangential vectors atpoints other than the points on the Y- and Z-axes are calculated (Steps7 and 8). Thus, farther from the point Q_(0,0), the larger the error inthe calculated value, and the sizes of the errors of the calculatedvalues are not symmetric with respect to the central point Q_(4,4) ofthe target surface 10 a through which the optical axis of the projectionobjective lens PL passes.

[0081] For this reason, the heights Z_(i,j) may be calculated in theaccordance with the following procedure. First, in step 2, the heightZ_(4,4) in the Z direction of the tangential vector at the point Q_(4,4)located at the center of the target surface 10 a is defined as 0. Insteps 3 to 6, the heights Z_(4,0) to Z_(4,3), Z_(4,5) to Z_(4,8), andZ_(0,4) to Z_(3,4), Z_(5,4) to Z_(8,4) in the Z direction of thetangential vectors at the points Q_(4,0) to Q_(4,3), Q_(4,5) to Q_(4,8),Q_(0,4) to Q_(3,4), and Q_(5,4) to Q_(8,4) on axes extending through thecentral point Q_(4,4) and parallel to the Y- or Z-axis are calculated.Thereafter, in steps 7 and 8, the heights Z_(i,j) (i≠4, j≠4) in the Zdirection of the tangential vectors at points other than the points onthe axes extending through the point Q_(4,4) and parallel to the Y-orX-axis are calculated.

[0082] When the distortion measurement points, i.e., the marks on thetest reticles, are not arranged on the lattice points of the squarelattices, the heights in the Z direction and the plane normal vectors atlattice points on square lattices located between the respectivemeasurement points are interpolated. More specifically, the height inthe Z direction and the plane normal vector at a lattice point can beobtained by summing the heights in the Z direction and the plane normalvectors at a plurality of measurement points surrounding these latticepoints while weighting them with the distances between the measurementpoints and the lattice points.

[0083] In above steps 1 to 8, only information inside the distortionmeasurement points is used. However, in order to further smooth thesurface of the distortion correction plate 10 serving as the targetmember, the lattice points may be set on the outer side (a side remotefrom the optical axis) of the principal ray passing points correspondingto the distortion measurement points, and the heights in the Z directionand the plane normal vectors at these lattice points may be extrapolatedfrom the height in the Z direction and the plane normal vector at theoutermost principal ray passing point.

[0084] The distortion correction plate 10 is removed from the projectionoptical apparatus shown in FIG. 3, and the surface of the removeddistortion correction plate 10 is machined based on surface shape dataof the distortion correction plate 10 which is calculated through steps1 to 8. The distortion correction plate 10 of this embodiment has arandom surface that waves irregularly, in order to correct the randomcomponent of the distortion. Accordingly, in this embodiment, apolishing machine as shown in FIG. 15 is used. A coordinate system asindicated in FIG. 15 is employed.

[0085] Referring to FIG. 15, the distortion correction plate 10 isplaced on a stage 21 movable in the X and Y directions, and the endportion of the distortion correction plate 10 is abutted against a pin21 a on the stage 21. A driver 22 for moving the stage 21 in the X and Ydirections is controlled by a controller 20. A detector 30 comprising anencoder, an interferometer, and the like is provided to the stage 21 todetect the position of the stage 21 in the X and Y directions when thestage 21 is moved. A detection signal output from the detector 30 istransmitted to the controller 20.

[0086] A polisher 23 is attached to one end of a rotating shaft 25through a holding portion 24 and is rotatable about the Z direction inFIG. 15 as the rotation axis. A motor 26 controlled by the controller 20is mounted to the other end of the rotating shaft 25. A bearing 27 thatrotatably supports the rotating shaft 25 is provided to a supportportion 28 fixed to a main body (not shown) to be movable in the Zdirection. A motor 29 controlled by the controller 20 is mounted to thesupport portion 28. When the motor 29 is operated, the bearing 27 ismoved in the Z direction, and accordingly the polisher 23 is moved inthe Z direction. The holding portion 24 for holding the polisher 23 isprovided with a sensor (not shown) which detects a contact pressurebetween the abrasion tray 23 and the distortion correction plate 10. Anoutput from this sensor is transmitted to the controller 20.

[0087] The operation of the polishing machine shown in FIG. 15 will bebriefly described. Surface shape data obtained through steps 1 to 8 isinput to the controller 20. Thereafter, the controller 20 moves thestage 21 in the X and Y directions through the driver 22 while itrotates the polisher 23. More specifically, the polisher 23 is moved onthe target surface 10 a of the distortion correction plate 10 in the Xand Y directions. At this time, the amount of abrasion of the targetsurface 10 a of the distortion correction plate 10 is determined by thecontact pressure between the target surface 10 a and the polisher 23 andthe residence time of the polisher 23.

[0088] An anti-reflection film is coated, by vapor deposition, on thedistortion correction plate 10 machined by the abrading machine shown inFIG. 15, and the machined distortion correction plate 10 is placed onthe holding member 11 of the projection optical apparatus shown in FIG.3. In the polishing machine of FIG. 15, the polisher 23 is fixed in theX and Y directions. However, the polisher 23 may be moved in the X and Ydirections in place of moving the stage 21 in the X and Y directions.Alternatively, a small tool (see FIG. 16) may be used in place of thepolisher 23.

[0089] With this embodiment described above, correction of the randomcomponent of distortion, which has conventionally been impossible onlywith adjustment of the respective optical members constituting theprojection optical system, can be performed easily.

[0090] In the above embodiment, as the plane-parallel plate having norefracting power is used as the distortion correction plate 10, thedecentering precision of the distortion correction plate can bemoderated. Then, even if positioning is performed by the holding member11 as shown in FIG. 4, i.e., even if positioning is determined by themachining precision of the holding member 11, sufficiently high opticalperformance can be achieved. As the distortion correction plate 10 is aplane-parallel plate, it can be machined easily. When a lens having apredetermined curvature is used as the distortion correction plate 10,this lens preferably has a low refracting power due to the reasondescribed above.

[0091] In the above embodiment, as the distortion correction plate 10 isarranged on the reticle R side (enlargement side) where the beam has asmaller numerical aperture, only shift of the principal ray isconsidered. However, when the distortion correction plate 10 is arrangedon the wafer W side (reduction side), the machining amount of thedistortion correction plate 10 is preferably determined by consideringthe influence of the size of the beam on the distortion correction plate10. Also, in order to further improve the precision of distortioncorrection, even if the distortion correction plate 10 is arranged onthe reticle R side, the machining amount is preferably determined byconsidering the influence of the size of the beam size on the distortioncorrection plate 10.

[0092] In the above embodiment, the distortion correction plate 10 ismounted in the optical path for measurement to decrease the adverseinfluence caused by the parts precision of the distortion correctionplate 10. However, for measurement, a dummy component different from thedistortion correction plate as the target member may be mounted in theoptical path. In this case, however, the parts precision of the dummycomponent must be high.

[0093] In the above embodiment, since the distortion correction plate 10is an optical member which is placed closest to the reticle of all theoptical members constituting the projection objective lens PL, theoperation of mounting and removing the distortion correction plate 10 inand from the optical path of the projection objective lens PL can beperformed easily.

[0094] In the above embodiment, the distortion correction plate 10 ispositioned with precision which is determined by the machining precisionof the holding member 11. In order to perform higher-precisioncorrection, a predetermined mark may be provided to part of thedistortion correction plate 10, so that the location of the distortioncorrection plate 10 with respect to the holding member 11 (with respectto the projection objective system PL) is optically detected. At thistime, the mark is desirably provided to the distortion correction plate10 at a position through which exposure light does not pass.

[0095]FIG. 16 briefly shows the adjusting method of the presentinvention that has been described so far. In FIG. 16, the distortioncorrection plate 10 is mounted in the optical path of the projectionobjective system PL, and the distortion is measured. Subsequently, theshape of the distortion correction plate 10 is calculated based on thismeasured distortion by using software that calculates an asphericalshape. Thereafter, the distortion correction plate 10 is machined byusing a small tool or the like so that it has the calculated shape. Whenthe distortion correction plate 10 machined in this manner is mounted inthe optical path of the projection objective system PL again, thedistortion on the surface of the wafer W is almost 0.

[0096]FIG. 17 briefly shows how to calculate the shape of the distortioncorrection plate 10 from distortion data. In FIG. 17, the amounts withwhich the plane normals at the respective points on the distortioncorrection plate 10 must be controlled are calculated based on thedistortion data obtained by measurement. Subsequently, the shape of acurved surface that the machining target should have is calculated suchthat it satisfies the control amounts calculated in this manner.

[0097] From the invention thus described, it will be obvious that theinvention may be varied in many ways. Such variations are not to beregarded as a departure from the spirit and scope of the invention, andall such modifications as would be obvious to one skilled in the art areintended for inclusion within the scope of the following claims.

[0098] The basic Japanese Application No. 009687/1995 (7-009687) filedon Jan. 25, 1995 is hereby incorporated by reference.

What is claimed is:
 1. A method of adjusting a projection opticalapparatus that projects an image of a first object on a second object,comprising: the first step of measuring a distortion component of saidprojection optical apparatus having a projection optical system and acorrection optical member which is arranged at a predetermined positionwith respect to said projection optical system; the second step ofcalculating, based on a measurement result of the first step, a surfaceshape that said correction optical member should have, the distortioncomponent of said projection optical apparatus being canceled to zerowhen said correction optical member has the surface shape that saidcorrection optical member should have; the third step of removing saidcorrection optical member from said projection optical apparatus andmachining said correction optical member so that the surface shape ofsaid correction optical member coincides with the surface shapecalculated in the second step; and the fourth step of re-arranging saidcorrection optical member machined in the third step at a position wheresaid correction optical member has been arranged in the first step.
 2. Amethod according to claim 1, further comprising the step, executed priorto the first step, of correcting components of various aberrations ofsaid projection optical apparatus that are symmetric with respect to anoptical axis of said projection optical system.
 3. A method according toclaim 1, wherein said projection optical system sequentially has a frontgroup, an aperture stop, and a rear group in an order named from a sideof said first object, and a distance between one of said front and reargroups through which a beam having a smaller numerical aperture passesand said correction optical member is smaller than a distance betweenthe other of said front and rear groups through which a beam having alarger numerical aperture passes and said correction optical member. 4.A method according to claim 1, wherein said projection optical systemsequentially has a front group, an aperture stop, and a rear group inthe order named from the side of said first object, and said correctionoptical member is arranged at a position close to said front or reargroup and farthest from said aperture stop.
 5. A method according toclaim 4, wherein an inequality d/f<0.07 is satisfied where f is thefocal length of one of said front and rear groups which is closer tosaid correction optical member, and d is a distance between, of opticalmembers belonging to said group closer to said correction opticalmember, one closest to said correction optical member and saidcorrection optical member.
 6. A method according to claim 1, wherein aninequality −0.005<Φ<0.005 is satisfied where Φ is the refracting powerof said correction optical member.
 7. A method according to claim 6,wherein the refracting power Φ of said correction optical member issubstantially zero.
 8. A method according to claim 7, wherein saidcorrection optical member is a plane-parallel plate.
 9. A methodaccording to claim 1, wherein said correction optical member arranged inthe first step is a dummy and is different from said correction opticalmember machined in the third step.
 10. A method according to claim 1,wherein the second step comprises: the step of calculating a normalvector at a first point of a surface shape that said correction opticalmember should have; the step of calculating a tangential vector at thefirst point that concerns a predetermined direction perpendicular to adirection of an optical axis of said projection optical system; the stepof setting a point remote from the first point in the predetermineddirection by a predetermined distance as a second point, and calculatinga product of an angle defined by the predetermined direction and thetangential vector and the predetermined distance; and the step of addingthe product to a height at the first point in the direction of theoptical axis of the surface shape that said correction optical membershould have, thereby obtaining a height in the direction of the opticalaxis of the surface shape at the second point.
 11. A method according toclaim 10, wherein a height is set at a predetermined value at thebeginning at a point through which the optical axis of said projectionoptical system passes, in the direction of the optical axis of thesurface shape that said correction optical member should have.
 12. Amethod according to claim 10, wherein a height in the direction of theoptical axis of the surface shape that said correction optical membershould have is obtained by a plurality of manners by changing thepredetermined direction, and a plurality of obtained values areaveraged.
 13. An exposure apparatus for transferring an image on anoriginal plate onto a photosensitive substrate, comprising: anillumination optical system for supplying light to said original plate;a first stage for supporting said original plate; a second stage forsupporting said photosensitive substrate; and a projection opticalapparatus, having a projection optical system and a correction opticalmember arranged at a predetermined position with respect to saidprojection optical system, for causing a position of said original platesupported by said first stage and a position of said photosensitivesubstrate supported by said second stage to be conjugated, wherein saidprojection optical apparatus is adjusted by a method comprising: thefirst step of measuring a distortion component of said projectionoptical apparatus; the second step of calculating, based on ameasurement result of the first step, a surface shape that saidcorrection optical member should have, the distortion component of saidprojection optical apparatus being canceled to zero when said correctionoptical member has the surface shape that said correction optical membershould have; the third step of removing said correction optical memberfrom said projection optical apparatus and thereafter machining saidcorrection optical member so that the surface shape of said correctionoptical member coincides with the surface shape calculated in the secondstep; and the fourth step of re-arranging said correction optical membermachined in the third step at a position where said correction opticalmember has been arranged in the first step.
 14. An exposure apparatusaccording to claim 13, wherein said projection optical systemsequentially has a front group, an aperture stop, and a rear group inthe order named from a side of said original plate, and a distancebetween one of said front and rear groups through which a beam having asmaller numerical aperture passes and said correction optical member issmaller than a distance between the other of said front and rear groupsthrough which a beam having a larger numerical aperture passes and saidcorrection optical member.
 15. An exposure apparatus according to claim13, wherein said projection optical system sequentially has a frontgroup, an aperture stop, and a rear group in the order named from theside of said original plate, and said correction optical member isarranged at a position close to said front or rear group and farthestfrom said aperture stop.
 16. An exposure apparatus according to claim15, wherein an inequality d/f<0.07 is satisfied where f is the focallength of one of said front and rear groups which is closer to saidcorrection optical member, and d is a distance between, of opticalmembers belonging to said group closer to said correction opticalmember, one closest to said correction optical member and saidcorrection optical member.
 17. An exposure apparatus according to claim13, wherein an inequality −0.005<Φ<0.005 is satisfied where Φ is therefracting power of said correction optical member.
 18. An exposureapparatus according to claim 17, wherein the refracting power Φ of saidcorrection optical member is substantially zero.
 19. An exposureapparatus according to claim 18, wherein said correction optical memberis a plane-parallel plate.